Is it possible to create web application using Qt?

Consider also using some HTTP server library like libonion or Wt. Wt is close in spirit to Qt. However, you won't use Qt itself. libonion is lower level (and you may want to use browser-side Web frameworks like e.g. JQuery or AngularJS with it).

If you already have some Web server, you could consider developing some FastCGI application in C++.

You surely need a good understanding of HTTP protocol and of HTML5 & AJAX.